Tthe force exerted by the wind on the sails of a sailboat is 390 n north. the water exerts a force of 180 n east. if the boat (including its crew) has a mass of 270 kg, what are the magnitude and direction of its acceleration? serway, raymond a.. college physics (p. 114). brooks cole. kindle edition.

a= 1.59 m/s² : Magnitude  of the acceleration

β = 65.22°   (north of east) : Direction of the acceleration

Explanation:

Conceptual analysis

We apply Newton's second law:

∑F = m*a (Formula 1)

∑F : algebraic sum of the forces in Newton (N)

m : mass in kilograms (kg)

a : acceleration in meters over second square (m/s²)

Problem development

The acceleration is presented in the direction of the resultant force applied .

Calculation of the resultant forces (R)

R= 429.5 N

We apply the formula (1) to calculate the magnitude of the acceleration(a) :

∑F = m*a , m= 270 kg

R= m*a

429.5 =270*a

a= 1.59 m/s²

Calculation of the direction of the acceleration (β)

β = 65.22°   (north of east)